$$x+(x+8)(x-3)(x+5) = 360$$
Answer
$$ \begin{matrix}x_1 = 5.50062 & x_2 = -7.75031+5.21495i & x_3 = -7.75031-5.21495i \end{matrix} $$
Explanation
$$ \begin{aligned} x+(x+8)(x-3)(x+5) &= 360&& \text{simplify left side} \\[1 em]x+(x^2-3x+8x-24)(x+5) &= 360&& \\[1 em]x+(x^2+5x-24)(x+5) &= 360&& \\[1 em]x+x^3+5x^2+5x^2+25x-24x-120 &= 360&& \\[1 em]x+x^3+10x^2+x-120 &= 360&& \\[1 em]x^3+10x^2+2x-120 &= 360&& \text{move all terms to the left hand side } \\[1 em]x^3+10x^2+2x-120-360 &= 0&& \text{simplify left side} \\[1 em]x^3+10x^2+2x-480 &= 0&& \\[1 em] \end{aligned} $$
This polynomial has no rational roots that can be found using Rational Root Test.
Roots were found using qubic formulas.
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Equations Solver